A pirate crew at the end of the day split the booty. The first pirate got 100 gold pieces, and 1/6 of the remaining booty. The second one got 200 gold pieces, and 1/6 of the remaining booty. The third one got 300 gold pieces, and 1/6 of the remaining booty. Ect. The last one only got, what if left from the booty.
At the end, every pirate had the same ammount of gold pieces (from the booty).
How many pirates were there, and how much was the booty.
Nth pirate gets 100N pieces so there must be 100N^2 pieces in all. This means that the first pirate gets 100N = 100+100(N-1)(N+1)/6. Subtracting 100 form both sides and dividing by (N-1) gives (N+1)/6 = 1 so N=5, each gets 500
